how to control an rgb node's color through a custom property
You can do it like any other custom property, but you have to set a different driver for each channel.
Expand the color wheel by clicking on the custom property color field, set it to R,G,B and right click on the first channel, choose Copy as new driver.
Then expand the RGB node color wheel by clicking on the color field, set it to R,G,B and right click in the first channel, choose Paste driver.
Now repeat that for the Green, Blue, and Alpha channel and the two colors will be synched.